On stability, passivity and reciprocity preservation of ESVDMOR

Abstract

The reduction of parasitic linear subcircuits is one of many issues in model order reduction (MOR) for VLSI design. This issue is well explored, but recently the incorporation of subcircuits from different modelling sources into the circuit model has led to new structural aspects: so far, the number of elements in the subcircuits was significantly larger than the number of connections to the whole circuit, the so called pins or terminals. This assumption is no longer valid in all cases such that the simulation of these circuits or rather the reduction of the model requires new methods. In Feldmann and Liu (ICCAD '04: Proceedings of the 2004 IEEE/ACM International Conference on Computer-Aided Design, 88-92, 2004), Liu et al. (ICCAD '05: Proceedings of the 2005 IEEE/ACM International Conference on Computer-Aided Design, 821-826, 2004; Integr. VLSI J. 41(2):210-218, 2008) the extended singular value decomposition based model order reduction (ESVDMOR) algorithm is introduced as a way to handle this kind of circuits with a massive number of terminals. Unfortunately, the ESVDMOR approach has some drawbacks because it uses the SVD for matrix factorizations. In Benner (Mathematics in Industry 14, 2009), Schneider (Matrix decomposition based approaches for model order reduction of linear systems with a large number of terminals, 2008) the truncated SVD (TSVD) as an alternative to the SVD within the ESVDMOR is introduced. In this paper we show that ESVDMOR as well as the modified approach is stability, passivity, and reciprocity preserving under reasonable assumptions. © 2011 Springer Science+Business Media B.V.